Abstract
This paper investigates a three-degrees-of-freedom (DoF) shimmy model of vehicle front wheels with steering system and dependent suspension. The contact models of rigid ground and elastic tire are analyzed from the viewpoint of predicting shimmy. Pacejka's magic formula and the delayed tire model are compared by means of stability charts in various parameter domains. Conclusions are obtained regarding the advantages and disadvantages of the use of the delayed tire model.
Issue Section:
Research Papers
References
1.
Broulhiet
,
G.
, 1925
, “
The Suspension of the Automobile Steering Mechanism: Shimmy and Tramp
,” Bull. Soc. Ing. Civ. Fr.
,
78
, pp. 540
–554
.2.
Von Schlippe
,
B.
, and
Dietrich
,
R.
, 1941
, “
Das Flattern Eines Bepneuten Rades
,” Bericht
,
140
, pp. 125
–147
.https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930093865.pdf3.
Somieski
,
G.
, 1997
, “
Shimmy Analysis of a Simple Aircraft Nose Landing Gear Model Using Different Mathematical Methods
,” Aerosp. Sci. Technol.
,
1
(8
), pp. 545
–555
.10.1016/S1270-9638(97)90003-14.
Thota
,
P.
,
Krauskopf
,
B.
, and
Lowenberg
,
M.
, 2009
, “
Interaction of Torsion and Lateral Bending in Aircraft Nose Landing Gear Shimmy
,” Nonlinear Dyn.
,
57
(3
), pp. 455
–467
.10.1007/s11071-008-9455-y5.
Li
,
Y.
,
Jiang
,
J. Z.
, and
Neild
,
S.
, 2017
, “
Inerter-Based Configurations for Main-Landing-Gear Shimmy Suppression
,” J. Aircr.
,
54
(2
), pp. 684
–693
.10.2514/1.C0339646.
Pouly
,
G.
,
Huynh
,
T. H.
,
Lauffenburger
,
J. P.
, and
Basset
,
M.
, 2008
, “
Active Shimmy Damping Using Fuzzy Adaptive Output Feedback Control
,” Tenth International Conference on Control, Automation, Robotics and Vision
(ICARCV
2008), Hanoi, Vietnam, Dec. 17–20, pp. 16
–22
.10.1109/ICARCV.2008.47954857.
Ran
,
S.
,
Besselink
,
I. J. M.
, and
Nijmeijer
,
H.
, 2014
, “
Application of Nonlinear Tyre Models to Analyse Shimmy
,” Veh. Syst. Dyn.
,
52
(Suppl. 1
), pp. 387
–404
.10.1080/00423114.2014.9015428.
Takacs
,
D.
,
Orosz
,
G.
, and
Stepan
,
G.
, 2009
, “
Delay Effects in Shimmy Dynamics of Wheels With Stretched String-Like Tyres
,” Eur. J. Mech.-A
,
28
(3
), pp. 516
–525
.10.1016/j.euromechsol.2008.11.0079.
Takacs
,
D.
, and
Stepan
,
G.
, 2009
, “
Experiments on Quasiperiodic Wheel Shimmy
,” ASME J. Comput. Nonlinear Dyn.
,
4
(3
), p. 031007
.10.1115/1.312478610.
Takacs
,
D.
, 2010
, “
Dynamics of Towed Wheels: Nonlinear Theory and Experiments
,” Ph.D. dissertation, University of Technology and Economics, Budapest, Hungary.11.
Takacs
,
D.
, and
Stepan
,
G.
, 2012
, “
Micro-Shimmy of Towed Structures in Experimentally Uncharted Unstable Parameter Domain
,” Veh. Syst. Dyn.
,
50
(11
), pp. 1613
–1630
.10.1080/00423114.2012.69152212.
Massaro
,
M.
, and
D J
,
C.
, 2012
, “
Neuromuscular-Steering Dynamics: Motorcycle Riders versus Car Drivers
,” ASME
Paper No. DSCC2012-MOVIC2012-8691. 10.1115/DSCC2012-MOVIC2012-869113.
De Falco
,
D.
,
Di Massa
,
G.
, and
Pagano
,
S.
, 2010
, “
Experimental Investigation on the Shimmy Phenomenon
,” Proc. Bicycle Motorcycle Dyn.
14.
Sharp
,
R. S.
, and
Limebeer
,
D. J. N.
, 2001
, “
A Motorcycle Model for Stability and Control Analysis
,” Multibody Syst. Dyn.
,
6
(2
), pp. 123
–142
.10.1023/A:101750821410115.
Koenen
,
C.
, 1983
, “
The Dynamic Behaviour of a Motorcycle When Running Straight Ahead and When Cornering
,” Ph.D. dissertation, Delft University, Delft, The Netherlands.16.
Tomiati
,
N.
,
Magnani
,
G.
,
Scaglioni
,
B.
, and
Ferretti
,
G.
, 2017
, “
Model Based Analysis of Shimmy in a Racing Bicycle
,” Proceedings of the 12th International Modelica Conference
, Prague
, Czech Republic, May 15–17, Linkping University Electronic Press, pp. 441
–447
.http://www.ep.liu.se/ecp/132/050/ecp17132441.pdf17.
Wei
,
D.
,
Jiang
,
T.
,
Chen
,
C.
,
Jiang
,
Y.
,
Pan
,
N.
, and
Pan
,
Z.
, 2017
, “
Hopf Bifurcation Character of an Interactive Vehicle-Road Shimmy System Under Bisectional Road Conditions
,” Proc. Inst. Mech. Eng., Part D
,
231
(3
), pp. 405
–417
.https://journals.sagepub.com/doi/full/10.1177/095440701664087418.
Mi
,
T.
,
Stepan
,
G.
,
Takacs
,
D.
, and
Chen
,
N.
, 2018
, “
Shimmy Model for Electric Vehicle With Independent Suspensions
,” Proc. Inst. Mech. Eng., Part D
,
232
(3
), pp. 330
–340
.10.1177/095440701770128219.
Pacejka
,
H. B.
, 1965
, “
Analysis of the Shimmy Phenomenon
,” Proc. Inst. Mech. Eng. Automob. Div.
,
180
(1
), pp. 251
–268
.10.1243/PIME_AUTO_1965_180_026_0220.
Lu
,
J. W.
,
Xin
,
J. Y.
,
Vakakis
,
A. F.
, and
Bergman
,
L. A.
, 2015
, “
Influences of System Parameters on Dynamic Behavior of the Vehicle Shimmy System With Clearance in Steering Linkage
,” J. Vib. Control
,
21
(2
), pp. 359
–370
.10.1177/107754631348378621.
Wei
,
D.
,
Xu
,
K.
,
Jiang
,
Y.
,
Chen
,
C.
,
Zhao
,
W.
, and
Zhou
,
F.
, 2015
, “
Hopf Bifurcation Characteristics of Dual-Front Axle Self-Excited Shimmy System for Heavy Truck Considering Dry Friction
,” Shock Vib.
,
2015
, p. 839801
.10.1155/2015/83980122.
Pacejka
,
H.
, 2006
, Tire and Vehicle Dynamics, 2nd ed.
,
Elsevier
, Oxford, UK.23.
Segel
,
L.
, 1966
, “
Force and Moment Response of Pneumatic Tires to Lateral Motion Inputs
,” ASME J. Eng. Ind.
,
88
(1
), pp. 37
–44
.10.1115/1.367088824.
Bachrathy
,
D.
, and
Stepan
,
G.
, 2012
, “
Bisection Method in Higher Dimensions and the Efficiency Number
,” Period. Polytech. Eng. Mech. Eng.
,
56
(2
), p. 81
.10.3311/pp.me.2012-2.0125.
Lehotzky
,
D.
, and
Insperger
,
T.
, 2016
, “
A Pseudospectral Tau Approximation for Time Delay Systems and Its Comparison With Other Weighted-Residual-Type Methods
,” Int. J. Numer. Methods Eng.
,
108
(6
), pp. 588
–613
.10.1002/nme.522526.
Beregi
,
S.
, and
Takacs
,
D.
, “
Analysis of the Tyre-Road Interaction With a Non-Smooth Delayed Contact Model
,” Multibody Syst. Dyn.
,
2017
(12
), p. 117
.10.1007/s11044-018-09636-227.
Beregi
,
S.
,
Takacs
,
D.
, and
Barton
,
D. A. W.
, 2017
, “
Hysteresis Effect in the Nonlinear Stability of Towed Wheels
,” ASME
Paper No. DETC2017-67722. 10.1115/DETC2017-6772228.
Bakker
,
E.
,
Nyborg
,
L.
, and
Pacejka
,
H. B.
, 1987
, “
Tyre Modelling for Use in Vehicle Dynamics Studies
,” SAE
Paper No. 870421.10.4271/87042129.
Hirschberg
,
W.
,
Rill
,
G.
, and
Weinfurter
,
H.
, 2007
, “
Tire Model TMeasy
,” Veh. Syst. Dyn.
,
45
(Suppl. 1
), pp. 101
–119
.10.1080/0042311070177628430.
Besselink
,
I. J. M.
, 2000
, “
Shimmy of Aircraft Main Landing Gears
,” Ph.D. thesis,
Delft University of Technology
, Delft, The Netherlands.31.
Li
,
S.
, and
Lin
,
Y.
, 2006
, “
Study on the Bifurcation Character of Steering Wheel Self-Excited Shimmy of Motor Vehicle
,” Veh. Syst. Dyn.
,
44
(Suppl. 1
), pp. 115
–128
.10.1080/0042311060086945332.
Clark
,
S. K.
(ed.), 1981
, “
Mechanics of Pneumatic Tires
,” U.S. Government Printing Office, Washington, DC.33.
Beregi
,
S.
,
Takacs
,
D.
, and
Stepan
,
G.
, 2016
, “
Tyre Induced Vibrations of the Car-Trailer System
,” J. Sound Vib.
,
362
, pp. 214
–227
.10.1016/j.jsv.2015.09.01534.
Abolfathi
,
A.
,
O'Boy
,
D. J.
,
Walsh
,
S. J.
,
Dowsett
,
A.
, and
Fisher
,
S. A.
, 2016
, “
Quantifying the Variability in Stiffness and Damping of an Automotive Vehicle's Trim-Structure Mounts
,” J. Phys.: Conf. Ser.
,
744
(1
), p. 012197
.10.1088/1742-6596/744/1/01219735.
Wilkes
,
J. C.
,
Wade
,
J.
,
Rimpel
,
A.
,
Moore
,
J.
,
Swanson
,
E.
,
Grieco
,
J.
, and
Brady
,
J.
, 2018
, “
Impact of Bearing Clearance on Measured Stiffness and Damping Coefficients and Thermal Performance of a High-Stiffness Generation 3 Foil Journal Bearing
,” ASME J. Eng. Gas Turbines Power
,
140
(7
), p. 072503
.10.1115/1.4038603Copyright © 2020 by ASME
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